Problems: Mandalas

File: Probs-Ch17.doc Chapter 17:

Problems: Mandalas

This file contains a selection of problems related to Chapter 17. These may be used when making up exams.

Classifying Mandalas  Using the code table below, identify the symmetry type Set 4: of the following mandalas.

(a) (b)

 Four figures are provided below. In the first column before each figure write a “1” or a “2” to indicate if the figure is one or two sided. In the second column, write (c) (d) the mandala type for the figure. Be sure to answer the question after the mandala table.

(a) ______

(e) (f) (b) ______

(c) ______

Code for Mandalas (d) ______Cn n-fold rotational symmetry (no reflect ional symmetry)

Dn Reflect ional symmetry and n-fold rotational symmetry D or D Bilateral symmetry only 1 Code for Mandalas N or C1 No symmetry Cn n-fold rotational symmetry (no reflect ional symmetry) ______D Reflect ional symmetry and Alternate Sets: n n-fold rotational symmetry Set 1: D or D1 Bilateral symmetry only

N or C1 No symmetry Question: What relationship do you see between the mandala type and whether the figure is one or two sided? Set 2: Describe the relationship.

______Set 3: Alternate Groups: Group 1:

1 Group 2:  Fold a sheet of paper in half, and then make two straight cuts starting and ending on the fold lines as pictured. (There are many ways to do these two cuts).

Fold and Cut Mandalas  If a double fold and cut figure is made as illustrated below, the result can be considered as a mandala. What type is this mandala? After unfolding, that kind of shape will you always have?

 Consider the following figure which can be created by folding and cutting a sheet of paper.

 Fold a sheet of paper in half, and then make two straight cuts starting and ending on the fold lines as pictured. (There are many ways to do these two cuts).

The four figures below represent a sheet of paper folded in various ways. Circle the paper that is correctly folded to produce the figure, and draw on it the outline along which you need to cut to give you the above figure. After unfolding, that kind of shape will you always have?

Single fold  Write down what type of symmetry the resulting Double fold figure will have.

Five fold Triple fold ______Alternate Figures:

Triple Fold

2  Take out a blank sheet of paper and, using fold and  Since one of the arrowheads is shaded, the following cut, make a copy of this figure. When you are done, put figure is a type D1 mandala. Shade more arrowheads so it your name on your cutout and turn it in with your test. becomes a D3 mandala.

______Alternate Figures:

 Jane made the template design shown below. She

claimed that it was a mandala of type D12, but one of her classmates disagreed because some of the arrows were darkened. What is the type of mandala?

 A sheet of dot-paper is double folded on the dashed lines as pictured. Imagine that the folded paper is cut along the dark line. Draw the rest of the shape that will result when the paper is unfolded.

______Alternate Figures:

______Alternate Figures:  Samantha made this mandala, and claimed that it

was a type D12, but Emily disagreed. Explain why you think she disagreed, and classify the mandala.

Your Explanation:

Shading and Classifying Template Designs  Since one of the arrowheads is shaded, the following  In the space below, make a template design with figure is a type D1 mandala. Shade more arrowheads so it symmetry type D8. becomes a D5 mandala.

3 Miscellaneous  Which of the seven types of quadrilaterals (square, kite, rhombus, rectangle, parallelogram, trapezoid, or isosceles trapezoid) have half-turn symmetry?  The mandala pictured below has symmetry code D4. Note that one angle of 35o is marked. Figure out the measure of angles a, b, and c. Note: Show your reasoning below!

o c  Which of the seven types of quadrilaterals (square, 35 kite, rhombus, rectangle, parallelogram, trapezoid, or isosceles trapezoid) have double fold and cut symmetry? a

 Make an example of a pentagon which has bilateral symmetry. True or Not

 For the following statements  If true, simply write true, or  If false, write false and draw an example showing the statement is  Ms. Jones was teaching second grade. Johnny was false. having trouble understanding the idea of reflect ional symmetry as demonstrated on the following card. (A) Mandalas always have a line of reflection.

(B) Fold and cut shapes are the same as shapes with bilateral symmetry.

(C) A mandala with C4 symmetry is a fold and cut shape. ______Alternate Statements:

In this course we have used at least three different ways Fold and cut shapes are the same as shapes with bilateral to describe or physically test for reflect ional symmetry. symmetry. Briefly describe three ways Ms. Jones could use to show Johnny this idea. A mandala cannot have both reflect ional and rotational symmetry. First way: It is not possible for a figure to have exactly five lines of symmetry.

One sided figures are the same as symmetric figures. Second way: If a mandala has two lines of symmetry, they must meet at right angles.

Third way:

4 Possible or Not

 For each of the following statements, decide if it is possible or not.  If it is possible, write POSSIBLE and draw a picture.  If it is not possible, write NOT and give a reason.

A fold and cut figure which makes a mandala of type D3?

A triangle which has three lines of symmetry?

A fold and cut figure of type C4?